In this paper, the authors propose a deformable modeling paradigm for 3D shape recovery from visual inputs such as volumetric data and 3D point clouds. The new model is capable of automatically evolving its shape to capture the geometric boundary of the data and simultaneously discover its underlying topological structure. The deformation behavior of the model is governed by partial differential equations (e.g. the weighted minimal surface flow) that are derived by the principle of variational analysis. Unlike the level-set approach, the model always has an explicit representation of geometry and topology.